Best Known (55, 55+18, s)-Nets in Base 3
(55, 55+18, 328)-Net over F3 — Constructive and digital
Digital (55, 73, 328)-net over F3, using
- 31 times duplication [i] based on digital (54, 72, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 18, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 18, 82)-net over F81, using
(55, 55+18, 463)-Net over F3 — Digital
Digital (55, 73, 463)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(373, 463, F3, 18) (dual of [463, 390, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 728, F3, 18) (dual of [728, 655, 19]-code), using
(55, 55+18, 15362)-Net in Base 3 — Upper bound on s
There is no (55, 73, 15363)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 67600 930072 758074 136167 235700 338103 > 373 [i]